The mayor has chosen sides in at least 10 primaries this year, as he looks to enact criminal justice changes and defeat left-leaning candidates.Most big-city mayors, especially those in the relative infancy of their tenures, typically try to avoid wading into fractious party primaries, mindful that their goal is to build consensus.Mayor Eric Adams of New York City does not subscribe to that theory.Just seven months into his first term, Mr. Adams, a Democrat, has injected himself into his party’s divide, making endorsements in roughly a dozen state legislative primaries.Mr. Adams has endorsed incumbents, upstart challengers, and even a minister with a history of making antisemitic and homophobic statements.Behind all the endorsements lies a common theme: The mayor wants to push Albany and his party away from the left, toward the center.“I just want reasonable thinking lawmakers. I want people that are responding to the constituents,” Mr. Adams said Thursday. “The people of this city, they want to support police, they want safe streets, they want to make sure people who are part of the catch-release-repeat system don’t continue to hurt innocent New Yorkers.”In Tuesday’s State Senate primary, the mayor has endorsed three candidates facing rivals backed by the Democratic Socialists of America. The mayor said the endorsements are meant to help elect people willing to tighten the state’s bail law, a move that he believes is needed to address an uptick in serious crime.Mr. Adams’s most striking endorsement might be his decision to back the Rev. Conrad Tillard, who has disavowed his remarks about gay people and Jews, over incumbent Senator Jabari Brisport, a member of the Democratic Socialists.The mayor, who proudly hires people with troubled pasts, said Mr. Tillard is a changed man. During a recent interview on WABC radio, Mr. Tillard said that Mr. Adams was elected with a “mandate” to make New York City safer.“I want to join him in Albany, and I want to join other legislators who have common sense, who realize that without safe streets, safe communities, we cannot have a thriving city,” he said.The mayor has also held a fund-raiser for Miguelina Camilo, a lawyer running against Senator Gustavo Rivera in the Bronx. Mr. Rivera was endorsed by Representative Alexandria Ocasio-Cortez, who has criticized Mr. Adams for some of his centrist views; Ms. Camilo is the candidate of the Bronx Democratic Party.In a newly created Senate district that covers parts of Queens, Brooklyn and Manhattan, the mayor has endorsed a moderate Democrat, Elizabeth Crowley, over Kristen Gonzalez, a tech worker who is supported by the Democratic Socialists and the Working Families Party. Mike Corbett, a former City Council staff member, is also running. The race has been flooded with outside money supporting Ms. Crowley.In Brooklyn, Mr. Adams endorsed incumbent Senator Kevin Parker, who is facing a challenge from Kaegan Mays-Williams, a former Manhattan assistant district attorney, and David Alexis, a former Lyft driver and co-founder of the Drivers Cooperative who also has support from the Democratic Socialists.Senator Kevin Parker, endorsed by the mayor, faces a Democratic Socialist opponent.Michael M. Santiago/Getty ImagesThree candidates — Mr. Brisport, Ms. Gonzalez and Mr. Alexis — whose rivals were supported by Mr. Adams said they are opposed to revising the bail law to keep more people in jail before their trials.“When it comes to an issue like bail reform, what we don’t want to have is a double standard where if you have enough money you can make bail and get out, but if you are poor or working class you don’t,” Ms. Gonzalez said.Mr. Brisport said that the mayor’s motive extends beyond bail and criminal justice issues.Mr. Adams, Mr. Brisport said, is “making a concerted effort to build a team that will do his bidding in Albany.”The mayor did not disagree.In his first dealings with Albany as a mayor, Mr. Adams fell short of accomplishing his legislative agenda. He had some victories, but was displeased with the Legislature’s refusal to accommodate his wishes on the bail law or to grant him long-term control of the schools, two issues central to his agenda.While crime overall remains comparatively low and homicides and shootings are down, other crimes such as robbery, assault and burglary have increased as much as 40 percent compared with this time last year. Without evidence, the mayor has blamed the bail reform law for letting repeat offenders out of jail.Under pressure from the governor, the Legislature in April made changes to the bail law, but the mayor has repeatedly criticized lawmakers for not going far enough.Mr. Adams has raised campaign money for Miguelina Camilo, center. Janice Chung for The New York Times“We passed a lot of laws for people who commit crimes, but I just want to see what are the list of laws we pass that deal with a New Yorker who was the victim of a crime,” Mr. Adams said. The mayor’s strategy is not entirely new. Mayor Michael R. Bloomberg sought influence by donating from his personal fortune to Republicans. Mayor Bill de Blasio embarked on a disastrous fund-raising plan to help Democrats take control of the Senate in 2014. But those mayors were interceding in general elections, not intraparty primaries.In the June Assembly primaries, Mr. Adams endorsed a handful of incumbents facing upstart challengers from the left. He backed Michael Benedetto, an incumbent from the Bronx who beat back a primary challenge from Jonathan Soto, who worked for, and was endorsed by, Ms. Ocasio-Cortez. Mr. Adams also endorsed Assemblywoman Inez E. Dickens in Central Harlem in her victorious campaign against another candidate backed by Ms. Ocasio-Cortez.“The jury is still out on how much endorsements matter, but they do matter for the person being endorsed,” said Olivia Lapeyrolerie, a Democratic political strategist and former aide to Mr. de Blasio. “It’s good to keep your friends close.”Mr. Adams’s influence is not restricted to his endorsements. Striving for a Better New York, a political action committee run by one of his associates, the Rev. Alfred L. Cockfield II, donated $7,500 to Mr. Tillard in May and more than $12,000 to Mr. Parker through August.The mayor’s efforts have come under attack. Michael Gianaris, the deputy majority leader in the Senate, said there is no need to create a new faction in the Senate that is reminiscent of the Independent Democratic Conference, a group of breakaway Democrats that allowed Senate Republicans to control the chamber until they were vanquished in 2018.“Eric Adams was never very good at Senate politics when he was in the Senate,” Mr. Gianaris said. “And apparently he hasn’t gotten much better at it.”It’s unclear how much influence Mr. Adams’s endorsements will have. Sumathy Kumar, co-chair of the New York City chapter of the Democratic Socialists of America, said that with the mayor’s lukewarm approval ratings, she’s betting that on-the-ground organizing will be the deciding factor in what is expected to be a low turnout primary.Mr. Parker said the mayor’s endorsement would be influential in his district and supported Mr. Adams’s push against the left wing of the party.“How many times do you have to be attacked by the D.S.A. before you realize you’re in a fight and decide to fight back?” Mr. Parker said.Emma G. Fitzsimmons contributed reporting. More